Visual methods for exploring multivariate spatio-temporal networks with application to health transport

Confirmation Report

Background

Analysing spatio-temporal network data is a contemporary research problem that has gained increasing interest in the health field, particularly within emergency medical services (EMS) and ambulance transfer systems. Such data capture spatial, temporal, and often multivariate information. The spatial component generally represents geographic locations or spatial geometries, while the temporal component records time-related information through timestamps or time intervals (Rao, Govardhan, and Rao 2012). In addition, the underlying network structure creates connections and multivariate dependencies between locations and transfers. While techniques exist to analyse spatial and temporal components separately, performing analysis, and perhaps more importantly, exploring these components in conjunction with the network structure, remains an open challenge.

Older individuals often require continuous support, including 24-hour care, assistance with daily tasks, and ongoing medical supervision. Thus, many reside in the residential aged care facilities (RACFs), which are specifically designed to provide this comprehensive care (Kearney and Winterbottom 2006). RACFs frequently rely on the ambulance services to facilitate the transfers of an individual to the hospital for both acute emergencies and planned/scheduled medical appointments. This rise in the number of transfers is partly due to population ageing (Harris and Sharma 2018), which puts incredible pressure on emergency medical services, where delay could lead to an increase in health risk (Harmsen et al. 2015). During the COVID-19 pandemic, lockdown measures and movement restrictions further disrupted the delivery of emergency services. The effects of lockdowns and rising transfer demand highlight the need for further analysis to improve the planning and utilisation of ambulance services.

The ambulance transfer data was provided by Alfred Health. The dataset included the following aspects: spatial, temporal, and multivariate information on each transfer. The spatial covers the location of the aged care facilities and the hospital (destination) in latitude and longitude. While the temporal provides the date of the transfers, which cover the period between January 2018 and May 2022. For multivariate information, it covers hospitals, aged care facilities, and patient-level details.

To gain insight into transfer patterns, data exploration using network representations linking RACFs and hospitals provides a powerful framework. However, most network research focuses primarily on topological properties, often treating them homogeneously and overlooking other important information, such as the association between variables (Cardenas et al. 2021; Fernández-Gracia et al. 2017). While network representation is suited to transfer data, overemphasising network topology can neglect the fundamental principles of data exploration. These limitations arise from the practical challenges of working with spatio-temporal network data, including data cleaning methods, particularly temporal information, the ease of data wrangling and subsetting, and the challenges of visualisation and inference. As a result, simple informative analyses, such as examining variable distributions, temporal trends, or bivariate relationships, are often underutilised, despite the ability to reveal key insights of the data. This underlines the need for an infrastructure that integrates network-based approaches with exploratory data analysis (EDA), enabling a comprehensive exploration of spatio-temporal transfer networks.

Studying how infectious diseases spread throughout the network (transfer between RACFs and hospitals) is important because the older population tend to face a higher risk of mortality during the outbreaks (Parohan et al. 2020). These patient transfers between facilities create ways for the disease to be transmitted across the systems, leading to rapid spread. Traditional compartmental infectious disease models assuming homogeneous or static structure do not adequately capture networks that change over time. In reality, ambulance transfers are highly dynamic, where these connections between facilities can change in response to the demand, constraints, and even outbreak conditions. Understanding these transmission dynamics is therefore crucial for devising effective policies to limit spread as well as identify high-risk facilities, critical transfer connections, and exposed periods.

Project 1: Developing Infrastructure for Exploratory Analysis of Multivariate Spatio-temporal Network with Application to Ambulance Transfers

Part A: Exploratory Data Analysis Infrastructure for Multivariate Spatio-temporal Network

Multivariate spatio-temporal network data has space, time, multiple variables, associations between different locations (which define the network), and multiple types of relationships (hospital to hospital or aged care to hospital, etc.) As these data become more accessible and complex, understanding their structure and dynamics is key to effective decision-making. A major challenge in analysing this data lies in the sheer amount of information it contains. Most of which is often overlooked due to the difficulty of switching between these dimensions. This infrastructure aims to support the exploration of multivariate spatio-temporal network data. The exploratory data analysis involves several key processes: data storage, cleaning, subsetting, and visualisation. The following section, therefore, reviews existing tools that support these processes and discusses their limitations.

Data Storage and Cleaning

Data cleaning is the first stage of a reliable analysis. Spatio-temporal data usually need to be checked for inconsistency of the temporal records, duplicated records, and spatial inaccuracies. Now, adding the network structure on top of that, such as nodes, edges, and their attributes, requires the network topology to be kept throughout the process. Typically, this stage involves tools such as dplyr (Wickham et al. 2023) for manipulating the data, tsibble (Wang, Cook, and Hyndman 2020) for validating the temporal inconsistency, sf (Pebesma 2018) for checking the coordinate inaccuracies, and igraph/network (Csárdi et al. 2026; Butts 2008) for keeping the network structure.

The tidygraph (Pedersen 2024b) package provides a tidy API for graph and network manipulation, where network data is thought of as two tidy tables, one for node and one for edge data. In tidy data (Wickham 2014), each variable has its own column, each observation has its own row, and each value has its own cell. These tables are then stored together within a tbl_graph object, which preserves the underlying network topology while allowing standard dplyr verbs to be applied. The interaction between node and edge tables is done through the use of a special function, activate(), which allows the user to switch between the two tables and apply dplyr operations such as mutate(), group_by(), and join operations as shown in Listing 1.

There are two main functions for creating tbl_graph object, as_tbl_graph() and tbl_graph(). The first function as_tbl_graph() takes in a different class of objects, such as data.frame, igraph, and network, then turns it into a tbl_graph object. While tbl_graph() takes in two data.frame objects, one for node and one for edge.

From the Listing 1, the difference between these two methods is that for the as_tbl_graph() function, it only needs the edges dataset, which means that all the multivariate information will only be on edge data and in the node data, it will only have the name (location). For the tbl_graph() function, the node variable can be explicitly stated, which can come in handy when there are attributes on the node dataset.

Listing 1: A function for creating a tbl_graph object. There are two main ways: first, using the edge list and second, using node and edge tables. The dplyr function will work normally, like it is on a tibble object, but requires an activate() function to switch between the two tables (node and edge).

as_tbl_graph(edges)

tbl_graph(nodes, edges)

graph |>
  activate(edges) |>
  mutate(year = lubridate::year(casedate))

# A tbl_graph: 815 nodes and 102073 edges
#
# A directed acyclic multigraph with 6 components
#
# Edge Data: 102,073 × 9 (active)
    from    to casedate     age gender diagnosis         daytype single_id  year
   <int> <int> <date>     <dbl> <chr>  <chr>             <chr>       <dbl> <dbl>
 1   575   659 2019-04-29    96 Female OTHER - SPECIFY   weekda…  10097915  2019
 2   514   628 2022-05-31    88 Female SHORT OF BREATH   weekda…  13485226  2022
 3   522   628 2020-10-03    90 Male   LACERATION        weeken…  11574122  2020
 4   562   633 2020-12-18    91 Female PAIN              weekda…  11813591  2020
 5   562   640 2018-02-05    89 Female SEPSIS            weekda…   8895777  2018
 6   562   633 2021-03-31    92 Female PAIN              weekda…  12134872  2021
 7   562   640 2021-04-22    92 Female SHORT OF BREATH   weekda…  12204603  2021
 8   562   633 2019-07-20    97 Female URINARY TRACT IN… weeken…  10340046  2019
 9   516   706 2021-01-13    98 Female NO PROBLEM IDENT… weekda…  11895939  2021
10   596   640 2020-07-04    90 Male   ALTERED CONSCIOU… weeken…  11319542  2020
# ℹ 102,063 more rows
#
# Node Data: 815 × 4
  name                        longitude latitude type 
  <chr>                           <dbl>    <dbl> <chr>
1 1 ABERDEEN STREET RESERVOIR      145.    -37.7 racf 
2 1 ADENEY STREET CAMPERDOWN       143.    -38.2 racf 
3 1 AITKEN AVENUE DONALD           143.    -36.4 racf 
# ℹ 812 more rows

For spatial networks, the sfnetworks package (van der Meer et al. 2024) extends tidygraph by allowing spatial geometries to be incorporated directly within the tbl_graph object. It is useful for dealing with complex geometry where edges are not straight-line connections, such as road or transport networks. The package also allows for the standard spatial operation within the sf package to be performed within the network context.

However, the tidygraph object does not provide direct support for time. For example, using a tsibble object as an edge table, which would allow temporal checks, including checking time intervals and missing values. Currently, these checks are performed prior to the creation of the tbl_graph. It introduces an important limitation, where common operations such as filling missing observations are done outside the network context and therefore do not preserve the network topology.

A basic requirement in cleaning temporal network data is the ability to check whether both nodes exist for a given edge at a specific time. In the case of a missing node, how should the edges associated with that node be imputed? A possible solution is to assume that no edges exist during that period, which may be reasonable in some cases but not in others. It highlights a key challenge in cleaning spatio-temporal network data, where temporal consistency and network structure should be considered jointly. Addressing these requires an object to ensure that both temporal attributes and the relational structure of the network remain coherent throughout the cleaning process.

Data Subsetting

Data subsetting is used to extract a subset of spatio-temporal network data based on spatial, temporal, and multivariate variables. It includes grouping data by time periods or regions, as well as filtering based on variable values and network characteristics (e.g., in-degree). Subsetting is particularly useful for in-depth analysis, where it may need data from all RACFs within a certain distance of a particular hospital or transfers occurring during the weekends.

In a network context, filtering operations need to account for topological dependencies between nodes and edges. When nodes are removed based on a condition, all edges incident to those nodes are also deleted (Figure 1). In contrast, when edges are removed, the nodes connected to those edges are preserved, since nodes can exist independently from an edge (Figure 2). The tidygraph supports these subsetting operations through the use of dplyr functions such as filter() and select(), illustrated in Listing 2, which are applied separately on nodes and edges while maintaining the condition of the underlying network. Similarly to the data manipulation, users will need to switch between the node and edge tables to subset based on their attributes.

Listing 2: A filtering method in tidygraph, where the activate() function allows the user to switch between the node and edge tables.

graph |>
  activate(edges) |>
  filter(between(year, 2020, 2021))

# A tbl_graph: 815 nodes and 48606 edges
#
# A directed acyclic multigraph with 59 components
#
# Edge Data: 48,606 × 9 (active)
    from    to casedate     age gender diagnosis         daytype single_id  year
   <int> <int> <date>     <dbl> <chr>  <chr>             <chr>       <dbl> <dbl>
 1   522   628 2020-10-03    90 Male   LACERATION        weeken…  11574122  2020
 2   562   633 2020-12-18    91 Female PAIN              weekda…  11813591  2020
 3   562   633 2021-03-31    92 Female PAIN              weekda…  12134872  2021
 4   562   640 2021-04-22    92 Female SHORT OF BREATH   weekda…  12204603  2021
 5   516   706 2021-01-13    98 Female NO PROBLEM IDENT… weekda…  11895939  2021
 6   596   640 2020-07-04    90 Male   ALTERED CONSCIOU… weeken…  11319542  2020
 7   279   769 2020-05-16    19 Male   POST ICTAL        weeken…  11183777  2020
 8   231   645 2020-08-06    46 Male   OTHER - SPECIFY   weekda…  11422186  2020
 9   231   645 2020-08-07    46 Male   OTHER - SPECIFY   weekda…  11415518  2020
10   265   657 2021-05-05    45 Male   NO PROBLEM IDENT… weekda…  12244819  2021
# ℹ 48,596 more rows
#
# Node Data: 815 × 4
  name                        longitude latitude type 
  <chr>                           <dbl>    <dbl> <chr>
1 1 ABERDEEN STREET RESERVOIR      145.    -37.7 racf 
2 1 ADENEY STREET CAMPERDOWN       143.    -38.2 racf 
3 1 AITKEN AVENUE DONALD           143.    -36.4 racf 
# ℹ 812 more rows

(a) Full network

(b) Node to remove

(c) Filtered network

Figure 1: An illustration of node filtering, such as can be done in tidygraph. The selection of a node can be made based on variables such as the facility type (RACF or Hospital). When a node gets filtered out, edges incident to it will also disappear.

(a) Full network

(b) Edges to remove

(c) Filtered network

Figure 2: An illustration of edge filtering, such as can be done in tidygraph. The selection of an edge can be made based on variables such as the transfer weekend. When an edge gets filtered out, nodes incident to it will still be kept.

Network Sampling

Another important aspect of subsetting is understanding how sampling methods perform on network data. Observational data are often not evenly distributed across multiple dimensions such as time, space, or variable groups. Some strata may contain more observations than others, and analysing these can directly impact the interpretation, as the larger group of strata may dominate the patterns seen. Sampling provides a way to subset the data while keeping it representative of the population. Stratified sampling, in particular, helps with an imbalance case by dividing the data into subgroups and sampling within each group, ensuring that all groups are represented in the sampled data.

In the network context, sampling methods are generally categorised into the following (Chuong Nguyen 2025):

• Node-based sampling selects a subset of nodes from the network and retains edges that are incident to the sampled nodes. This method is efficient and is usually implemented in large-scale studies (Ben-Eliezer et al. 2022). It often fails to capture important global structural properties such as connectivity and clustering.

• Edge-based sampling samples a subset of edges directly and includes the nodes incident to those edges. This method is better at preserving structural pattern (Jiao 2024). However, it may introduce bias towards selecting nodes with higher degrees, resulting in biased sampled data.

There are many additional methods for sampling. Hu and Lau (2013) provides a comprehensive survey and taxonomy of graph sampling approaches, which are outside the scope of this project.

(a) Full network

(b) Sampled edge

(c) Sampled network

Figure 3: An illustration of edge-based sampling, such as can be done in tidygraph. The edges set will get sampled, then only include the nodes incident to those edges. This method will be biased towards selecting nodes with higher degrees.

The tidygraph package provides a method for sampling the data for a tbl_graph object through a sample_n() function, although it is now recommended to use slice_sample() instead. A further limitation of the tbl_graph is that it does not directly support stratified (i.e., group_by) sampling. Instead, the tbl_graph object needs to be converted back to tibble (Müller and Wickham 2025), performing stratified sampling on the node or edge table, and then filtering the original network based on the sampled nodes or edges (Listing 3). This limitation shows that sampling operations for network objects can still be improved.

Listing 3: A code comparison between sampling and stratified sampling on edges. The tidygraph supports edge sampling using the sample_n() function, but with stratified sampling, it does not. This makes it much harder to code stratified sampling.

set.seed(1)

# Edges sampling
graph |> 
  activate(edges) |> 
  sample_n(size = 20)

# Stratified edges sampling
edges_kept <- graph |> 
  activate(edges) |> 
  as_tibble() |> 
  group_by(daytype) |> 
  sample_n(size = 10) |> 
  pull(single_id)

graph |> 
  activate(edges) |> 
  filter(single_id %in% edges_kept) |> 
  activate(nodes) |> 
  filter(!node_is_isolated())

# A tbl_graph: 33 nodes and 20 edges
#
# A rooted forest with 13 trees
#
# Node Data: 33 × 4 (active)
   name                                           longitude latitude type 
   <chr>                                              <dbl>    <dbl> <chr>
 1 120 MCCRACKEN STREET ESSENDON                       145.    -37.7 racf 
 2 2 CLARKE STREET ABBOTSFORD                          145.    -37.8 racf 
 3 220 MIDDLEBOROUGH ROAD BLACKBURN SOUTH              145.    -37.8 racf 
 4 23 FOREST DRIVE FRANKSTON NORTH                     145.    -38.1 racf 
 5 242 JELLS ROAD WHEELERS HILL                        145.    -37.9 racf 
 6 27 SHIERLAW AVENUE CANTERBURY                       145.    -37.8 racf 
 7 27 VICTORIA STREET ELSTERNWICK                      145.    -37.9 racf 
 8 359 NARRE WARREN NORTH ROAD NARRE WARREN NORTH      145.    -38.0 racf 
 9 41 LANDSBOROUGH STREET WARRAGUL                     146.    -38.2 racf 
10 45 SILVAN ROAD WATTLE GLEN                          145.    -37.7 racf 
# ℹ 23 more rows
#
# Edge Data: 20 × 9
   from    to casedate     age gender diagnosis          daytype single_id  year
  <int> <int> <date>     <dbl> <chr>  <chr>              <chr>       <dbl> <dbl>
1    15    21 2022-04-04    65 Male   NO PROBLEM IDENTI… weekda…  13309866  2022
2     1    24 2020-08-22    97 Female FEBRILE            weeken…  11456547  2020
3     9    30 2020-12-20    51 Female PSYCHIATRIC EPISO… weeken…  11821121  2020
# ℹ 17 more rows

As discussed in Section 2.1.2, nodes in a network can exist independently without incident edges. Thus, the edge-based sampling does not automatically remove nodes that become isolated after sampling. To remove these nodes, they must be explicitly removed by filtering the node table using the node_is_isolated() function.

Data visualisation

Data visualisation helps reveal patterns, anomalies and relationships that may not be apparent from numerical summaries alone. Network data is often viewed as connections or flows between nodes/locations, and network-based visualisation allows for easier communication to a broader audience. For a simple network without spatial coordinates, placing nodes and edges in a visualisation requires the use of a graph layout algorithm, such as the Kamada-Kawai layout (Kamada and Kawai 1989). Depending on the chosen algorithm, the positions of nodes and edges can be different even on the same network dataset. With spatial information, visualising these becomes more straightforward, as longitude and latitude can be used to specify the actual location of the nodes, with edges represented as lines connecting these locations.

Visualising multivariate spatio-temporal network data can be challenging. When spatial information is available, the decision to incorporate it into the visualisation is important. On one hand, spatial information allows nodes to be mapped to geographic space, making it easier to infer where nodes are located. On the other hand, omitting spatial information can help reveal non-spatial patterns in the network. Other problems arise when data are highly concentrated in urban areas, making it hard to perceive patterns, or when temporal information is added. A common approach for handling time is facetting, but comparing them requires many back-and-forths. Another possible solution is to animate the network visualisation.

simple_graph |> 
  ggraph(x = long, y = lat) +
  geom_sf(data = vic_map, color = "white") +
  geom_edge_link(alpha = 0.1) +
  geom_node_point(aes(color = category)) +
  scale_color_brewer(name = "Facility", palette = "Set1")

Figure 4: An ambulance transfer network in Victoria between residential aged care facilities and hospitals. The nodes are mapped to the spatial location (latitude and longitude), while edges are the connections between nodes. It can be difficult to observe patterns, since most of the nodes are located within the Melbourne area.

The main limitation of static network visualisation is the restricted amount of information that can be shown in a single figure. The current tool for network visualisation in R is the ggraph package (Pedersen 2024a), which extends the ggplot2 package (Wickham 2016) to support relational data structures such as networks, graphs, and trees. The ggraph package is effective at visualising static networks, offering a range of layout algorithms for placing the node locations while keeping the same familiar ggplot2 syntax. The support for interactive network visualisation with ggraph is currently limited. The reason static network visualisation is hard is that the amount of information that can be mapped to the visualisation is limited within a single figure. As shown in Figure 4, just a simple network representation can already become cluttered quickly. Answering detailed questions such as the number of transfers between a specific RACF and Hospital, or the name of a particular RACF, is difficult using static visualisation alone. Interactive visualisation helps with these limitations by layering additional information onto the visualisation, allowing for further exploration.

interactive_vis <- simple_graph |>
  mutate(name = str_remove(name, "'")) |>
  ggraph(x = long, y = lat) +
  geom_sf(data = vic_map, color = "white") +
  geom_segment_interactive(
    data = simple_graph |> activate(edges) |> as_tibble() |> mutate(id = row_number()),
    alpha = 0.2,
    aes(x = long_racf,
        y = lat_racf,
        xend = long_hosp,
        yend = lat_hosp,
        tooltip = weight,
        data_id = id)) +
  geom_point_interactive(aes(x = x,
                             y = y,
                             color = category,
                             tooltip = name,
                             data_id = name)) +
  scale_color_brewer(name = "Facility", palette = "Set1")

girafe(ggobj = interactive_vis,
       options = list(
         opts_hover(css = "fill:lightblue;stroke:grey;stroke-width:0.5px"),
         opts_zoom(min = 0.5, max = 3)
       ))

Figure 5: An interactive ambulance transfer network in Victoria between residential aged care facilities and hospitals. The extra information added to the nodes is the location name, and for edges, the number of transfers. This information will be visible when hovering over the node or edge. Using interactive makes it easier to explore the network without adding too much information to the plot.

The ggiraph package (Gohel and Skintzos 2025) provides an interactive element to the visualisation through the ggplot2 extension. Creating interactive network visualisations, therefore, typically requires combining ggraph for layout construction with ggiraph for interactivity. Getting this to work together requires an insight into how ggraph works, which is not a seamless implementation. For example, ggraph provides geom_node_* and geom_edge_* functions for nodes and edges geometry, respectively, but these do not natively support interactivity. To make nodes interactive, geom_point_interactive() needs to be used instead of geom_node_point(). Making edges interactive is more complex as it requires the use of geom_segment_interactive() and mapping the start and end coordinates (x, y, xend, yend) for each edge. By that point, if both node and edge need interactivity, then ggraph is not needed, and instead the node and edge can be treated as a different dataset and implement geom_point and geom_segment for drawing the node and edge.

Next steps

• I will be creating a new data object and turning it into an R package.

• The temporal data are not easy to clean currently with tidygraph. As a result, issues such as filling missing timestamps and handling inconsistent time periods are currently handled outside the network context, which may affect the network’s validity. Therefore, the new data object needs to integrate temporal and network topology jointly.

• The current data sampling method is limited, with most methods working outside the tidygraph object. Although many tools already work with tibble, its functionality requires writing a method for tbl_graph because tidygraph converts igraph into tibble. Therefore, the new data object should be built on top of tibble.

• Data visualisation capabilities are constrained by the ggraph package, as layout calculations are handled internally, making it difficult to access and reuse layout information when extending the visualisation method (e.g., interactive visualisation). Therefore, the new data object will be designed to work directly with the ggplot2 package for better expansion and application of additional geoms for network visualisation.

Part B: An Exploratory Analysis of Ambulance Transfer in Victoria

Ambulance and emergency medical services play a critical role in transferring older individuals from residential aged care facilities (RACFs) to hospitals. These transfers form a links between RACFs and hospitals across space and time, and are associated with multiple variable such as age, sex, and reason of transfer. Exploratory analysis provides an initial step in examining ambulance transfer data by reveling pattern, anomalies, and relationships. This data can be represented as a multivariate spatio-temporal network, where facilities are represented as nodes and ambulance transfers as time-varying edges.

During the COVID-19 pandemic, government-imposed lockdowns created significant challenges for ambulance services. Previous studies have shown that the pandemic affected the transfer of older individuals from residential aged care facilities to hospitals (Wyer et al. 2024; Nair et al. 2023; Botan et al. 2023). These restrictions limited ambulance availability and highlighted potential vulnerabilities in the reliance on ambulance transfers for aged care residents. Examining ambulance efficiency and transfer volumes during lockdown periods can inform strategies to improve system resilience and preparedness for future emergencies.

Transfer distance

To quantify the ambulance transfer, instead of just looking at the number of transfers, the distance travelled from the aged care facilities to the hospital is considered. The Euclidean distance will be used to calculate a transfer distance. It is the shortest distance between two points based on the latitude and longitude. This measure should give a reasonable estimate for less computing compared to the actual road distance. Note that the limitation is that it ignores the actual street network distance, which is not a straight line, and therefore, the distance between the RACF and the hospital will generally be longer.

Figure 6: Histogram of ambulance transfer distances for emergency and scheduled cases, with the median indicated by the blue line and the first and third quartiles shown in red. The distributions for emergency and scheduled transfers are similar, with no large difference between the two groups.

From Figure 6, the median is lower for the emergency transfer compared to scheduled transfers, but not much difference in terms of their distribution. However, there are transfers with zero distance in the data, which might suggest either a data entry error or that the aged care facilities and hospitals are co-located (i.e., located next to each other). In the latter case, this might suggest that the transfer may not be necessary. After filtering the distance data to zero and going through them manually, it can be seen that the aged care facility and hospital are indeed in the same location.

Generally, transfers of the patient should be done quickly, which means sending them to the closest hospital available. It could also explain why some RACFs have a zero transfer distance. Though when the co-located hospital cannot handle emergency cases, the ambulance will need to transfer patients to the nearest hospital with an emergency department. It can be verified using the hospital data, which includes a column indicating whether the hospital has an emergency department. To further analyse this, the distances will be calculated between RACFs and hospitals across all possible combinations to identify which RACFs are located next to hospitals. After the calculation, the RACFs will be categorised into two groups: RACFs close to hospitals and those otherwise.

Figure 7: Histogram of ambulance transfer distances for emergency and scheduled cases grouped by co-located RACF. The median is shown in a vertical blue line, while the first and third quartiles are shown in red. The median transfer distance for the co-located RACF is much higher than that of others.

Figure 8: The location of the RACF with the co-located RACF highlighted. The plot shows where all the RACFs are located in Victoria, with the one highlighted as the co-located facility. Most of the co-located facilities are in the regional area, with only a few in the Melbourne area.

The expectation of the transfer distance for the co-located RACF would be shorter than that of the other RACFs. However, as shown in Figure 7, the median transfer distance for the co-located RACF is higher. From Figure 8, it can be seen that there are many more co-located RACFs in the regional area than in the Melbourne area, which might explain the bimodality observed in Figure 7. This bimodality is likely caused by the longer travel distances for regional RACFs compared to those in Melbourne.

To highlight this regional effect, a sample of RACFs will be visualised on a map. The sampling is used to reduce edge clustering while still representing the observational data, making it easier to observe patterns. Additionally, since there are many facilities inside the Melbourne area, hospitals in Melbourne will be grouped based on their emergency capabilities.

Figure 9: The sampled co-located RACF transfer network, where the Melbourne hospital is grouped. These facilities are placed according to their spatial coordinates (latitude and longitude), with a line representing the transfers and alpha representing the transfer volume. Most patients are sent to Melbourne hospitals.

Figure 10: The sample co-located RACF transfer network, where the Melbourne hospital is grouped on the non-spatial layout. The nodes are placed based on the stress layout, which helps spread out the nodes. The transfer of the patient from regional RACFs to Melbourne is clearer, and there are two clusters of transfers.

From Figure 9, it can be observed that the longer median travel distances shown in Figure 7 are caused by the regional RACFs located in the regional area. Using spatial coordinates helps identify this pattern. However, this example also shows why mapping a network directly onto its spatial coordinates may not always be ideal. If the main focus of the plot is to highlight that most patients are transferred to Melbourne hospitals, this is not immediately clear in the spatial visualisation. Longer edges tend to attract more visual attention, and overlapping edges further obscure the transfer patterns.

In contrast, Figure 10 shows the same network but using a graph-based layout instead. This representation makes the pattern of transfers to Melbourne hospital much clearer, and the two clusters are more distinctly separated. This comparison highlights the importance of choosing between spatial and graph-based layouts.

Extending this to interactive visualisation is not straightforward. In the case of spatial plots, node locations are given in the data, making it easier to add interactivity using functions such as geom_point_interactive(). For a graph layout plot, while nodes can be made interactive, the edges are more difficult. It is because the layout positions are calculated internally within ggraph, making it challenging to extract and reuse layout information for interactive edges using functions such as geom_segment_interactive().

Following this, transfer reasons, such as dispatch type diagnosis, will be explored. To make comparison and interpretation easier, the transfer distance will be grouped into four categories: zero-distance (co-located facilities), short-distance (between 0 and 10km), medium-distance (between 10km and 50km), and long-distance (above 50km).

Table 1: The dispatch reason frequency table for different distance categories. These tables display the top seven common dispatch reasons for each category. The common dispatch reason for zero and medium distances is urgent transfers, while medium to long distances is mental health.

(a) Zero Distance

dispatch	n
AMBULANCE-URGENT WITHIN 25 MINS	18
AMBULANCE-CRITICAL	10
DR REQUESTING ATTENDANCE WITHIN 25 MIN	9
MENTAL HEALTH: ACUTE PROBLEMS	7
NEPT 000 EVENT TO ERTCOMM	6
NEPT BOOKED EVENT TO ERTCOMM	6
CLINICIAN-ACTIONED MEDIUM ACUITY EVENT	5

(b) Short Distance

dispatch	n
AMBULANCE-URGENT WITHIN 25 MINS	88
DR REQUESTING ATTENDANCE WITHIN 25 MIN	72
CLINICIAN-ACTIONED MEDIUM ACUITY EVENT	51
EMERGENCY DEPT TRANSFER - ON DAY	47
NO CONSENT-NOT URGENT/NO ASP 1-HOUR	31
AMBULANCE-CRITICAL	30
UNCONSCIOUS/FAINTING, NOT ALERT	21

(c) Medium Distance

dispatch	n
MENTAL HEALTH: NON URGENT	116
MENTAL HEALTH: ACUTE PROBLEMS	95
AMBULANCE EMERGENCY MULTILEG	80
AMBULANCE-URGENT WITHIN 25 MINS	78
EMERGENCY DEPT TRANSFER - ON DAY	61
CLINICIAN-ACTIONED MEDIUM ACUITY EVENT	53
NEPT BOOKED EVENT TO ERTCOMM	50

(d) Long Distance

dispatch	n
CLINICIAN-ACTIONED MEDIUM ACUITY EVENT	171
MENTAL HEALTH: ACUTE PROBLEMS	145
MENTAL HEALTH: NON URGENT	110
AMBULANCE EMERGENCY MULTILEG	85
CLINICIAN-ACTIONED LOW ACUITY EVENT	57
EMERGENCY DEPT TRANSFER - ON DAY	57
AMBULANCE-URGENT WITHIN 25 MINS	55

Table 2: The diagnosis frequency table for different distance categories. These tables display the top seven common diagnosis for each category. The common diagnosis for zero and medium distances is pain, while medium to long distances is psychiatric episode.

(a) Zero Distance

diagnosis	n
PAIN	12
FRACTURE/S	10
OTHER - SPECIFY	10
NO PROBLEM IDENTIFIED	9
PSYCHIATRIC EPISODE	9
SEPSIS	7
LACERATION	6

(b) Short Distance

diagnosis	n
PAIN	78
OTHER - SPECIFY	52
SEPSIS	30
FEBRILE	26
ALTERED CONSCIOUS STATE	21
FRACTURE/S	20
INFECTION - OTHER / NOT LISTED	18

(c) Medium Distance

diagnosis	n
PSYCHIATRIC EPISODE	174
OTHER - SPECIFY	84
PAIN	81
SUICIDAL IDEATION	62
FRACTURE/S	49
UNKNOWN PROBLEM	35
NO PROBLEM IDENTIFIED	29

(d) Long Distance

diagnosis	n
PSYCHIATRIC EPISODE	175
OTHER - SPECIFY	138
PAIN	90
SUICIDAL IDEATION	73
FRACTURE/S	59
ACUTE CORONARY SYNDROME	48
UNKNOWN PROBLEM	34

Next steps

• Add road distance to the dataset as an additional distance comparison. Also, including an indicator for aerial transfers can be helpful since aerial transport typically takes less time to transfer the patient to the hospital.

• Conduct a more in-depth analysis of the differences between emergency and scheduled transfers. The initial result (Figure 6) shows that there is not much difference between emergency and scheduled in terms of descriptive statistics and distribution. Further analysis would help to see if there are potential confounding variables.

• Analyse the potential overuse of ambulance callouts. Ideally, the resources should not be overused in non-emergency situations, identifying potential overuse would allow for better resource allocation when needed (e.g., emergency state).

• Examine the temporal patterns, such as peak demand for transfers. It would help inform policymakers about when additional ambulance resources are needed to prevent a system shortage.

• Assess the impact of COVID-19 on transfer patterns. Understanding how COVID-19 affected the system would support future planning in the event of another pandemic or disruption.

• Consider the implications for policymakers, such as the effects of a hospital shutdown. During the disease outbreaks, some hospitals may need to reserve their resources for specific cases, or the hospital is at full capacity. Understanding how this affects the transfer network would be useful for planning.

Project 2: Dynamics Infectious Disease Modelling using a Generalised Ambulance Model

Part A: Generalised Ambulance Model

This project focuses on understanding the impact of any changes in the ambulance transfer network on the spread of infectious diseases, particularly among older populations in residential aged care facilities. Ambulance transfer creates a way in which infections can be transmitted throughout facilities and hospitals (Gruber et al. 2013). Variations in transfer volume, patterns, or constraints can alter the structure of the network and, in turn, influence outbreak dynamics.

Statistical Network Models Review

There is a wide range of statistical network models, and the choice of model depends on the specific application. In infectious disease research, understanding the underlying contact network is therefore particularly important (Silk et al. 2017).

• Exponential Random Graph Model (ERGM): An ERGM is used to study the structure of network data by modelling the probability of observing a given network as a function of network structure and the characteristics of individuals (nodes) within the network (Robins et al. 2007). An advantage of ERGM is their ability to include individual traits (e.g., sex and age), which can be used to explain connection patterns and the likelihood of interacting with similar individuals. A limitation of the model is its lack of flexibility in specifying interaction terms, which is possible but not straightforward. ERGM can be fitted using the ergm R package (Pavel N. Krivitsky et al. 2023). For dynamic networks, temporal extensions such as the temporal exponential random graph model can be fitted using the btergm package (Leifeld, Cranmer, and Desmarais 2018).

• Latent Space Model: Latent space models provide an alternative method to ERGMs for modelling relational data. These models basically work like generalised linear models for edge values, while controlling for the network dependence by placing nodes in k-dimensional space according to their social network distance (Hoff, Raftery, and Handcock 2002; Pavel N. Krivitsky et al. 2009). The advantage of this model is its simpler implementation and fitting compared to ERGMs. However, interpretation of model coefficients can be challenging if the position of nodes in latent space covaries with values of nodal attributes (Cranmer et al. 2017). Latent space model can be fitted using the latentnet package (Pavel N. Krivitsky and Handcock 2008).

There has also been research using a spatio-temporal point process model to study ambulance demand rather than modelling the network structure. However, such work has primarily focused on ambulance deployment planning rather than transmission or transfer networks (Zhou et al. 2015).

Part B: Dynamics Infectious Disease Modelling

Infectious disease dynamics describe how the disease is spread and evolves within the population over time. These dynamics depend on the contact between individuals or groups, movement between locations, and the timing of infection and recovery. Traditional compartmental models, such as susceptible-infectious-recovered (SIR) or susceptible-exposed-infectious-recovered (SEIR), are often used to represent the disease progression within and between groups. Through this modelling, policymakers can conduct scenario analyses on the ambulance transfer network. For example, these models can be used to assess how an outbreak evolves if a particular hospital becomes unavailable due to an outbreak and how this disruption affects disease transmission across the system.

Using a simulated network as input to an infectious disease transmission model allows disease spread to occur both within facilities (RACFs and hospitals) and between facilities through ambulance transfers. Similar approaches have been explored in the literature. However, rather than using the simulated network, it uses a point process model to predict demand and then uses this output as input to an infectious disease model (Amaral, González, and Moraga 2023).

Timeline

Progress Update

Project 1A) Data cleaning and subsetting

• Explored multiple network analysis software, including tidygraph, igraph, and network for comparison (Section 2.1.1).

• Apply the above software on Caribou dataset, with the main focus on the temporal data gap that affects total distance travelled calculations.

• Considering imputation strategies for temporal network data to address missingness (Section 2.1.1).

Project 1A) Data visualisation

• Experiment with crosstalk to create linked, side-by-side visualisations combining network and simple descriptive plot.

• Constructed a supervisor-student relationship network to understand network theory.

• Explored ggiraph for interactive network visualisations (Section 2.1.4).

Project 1B) Exploratory data analysis

• Preliminary analysis of the ambulance transfer efficiency (Section 2.2.1)

Project 2A)

• Try a statistical network model such as ergm and intergraph for switching between igraph and network

Figure 11: A Gantt chart of my PhD project timeline. The sub-project name is shown alongside the expected timeline. Project 1 is planned to finish by the end of this year, and Project 2 is planned to finish by the end of next year.

Planned conferences

The following is a list of conferences that I will be targeting to attend and showcase the work.

• ANZIAM Conference (Feburary 2027)

• useR! Conference (2027)

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Botan, Vanessa, Graham Law, Despina Laparidou, Viet-Hai Phung, Ffion Curtis, Gregory Whitley, Joseph Akanuwe, et al. 2023. “PP63 Variations in the Number of Ambulance Attendances to Care Homes Before and During Covid-19 Pandemic: An Interrupted Time Series Analysis.” BMJ Publishing Group Ltd; the British Association for Accident ….

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